What is the Radius of Convergence for ∑[(2n+1)/2n] x^n?

kgarcia3
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Homework Statement



Find the radius of convergence of the following power series: ∑_(n=0)^∞[(2n+1)/2n] x^n)

Homework Equations



Ratio Test: lim_n->inf (a_n+1 / a_n)

The Attempt at a Solution



I got a big ugly fraction that involved both n and x
 
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Show us what you got.
 
kgarcia3 said:

Homework Statement



Find the radius of convergence of the following power series: ∑_(n=0)^∞[(2n+1)/2n] x^n)

Homework Equations



Ratio Test: lim_n->inf (a_n+1 / a_n)

The Attempt at a Solution



I got a big ugly fraction that involved both n and x

You should be able to get a second degree polynomial on the numerator and denominator... then apply L'Hopital rule.. why not show us the fraction you've gotten
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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